Translation:The neighbours invited us to look at their new TV set.
vidi = to see (vido = sight, view), percepti per la okuloj.
rigardi = to look (rigardo =look, view), fiksi la okulojn al iu direkto/objekto.
spekti = to watch to spectate (spektanto: spectator), atenti per la vido kaj aŭdo tion, kio estas prezentata. 'Spekti' as a special form of 'rigardi' is less used.
I think this isn't settled yet. From my experience, I can tell you that, here in the U.S., many women in the world of online dating -- I would bet this applies to men too, but I'm not looking at men's dating profiles -- specify that, on the one hand, they either don't own a TV or don't watch TV and, on the other hand, will list their favorite TV to watch on their computers / tablets. Which I always find very strange, particularly since making a point of stating that you don't own something as ubiquitous as a TV or automobile is, at least in this country, usually a form of bragging, usually about how virtuous/wise/non-materialistic/ecologically sound/non-consumer-oriented one is.
I played the sound many times and still couldn’t hear the “nin” properly. I knew there had to be something there and guessed right. This happens sometimes to me in English too, so I am not complaining about the clarity of the recording, nor will I report it. In English I usually have a context to make the correct guess. In Duolingo, with a single sentence, it is harder.